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June, 1986 An Efron-Stein Inequality for Nonsymmetric Statistics
J. Michael Steele
Ann. Statist. 14(2): 753-758 (June, 1986). DOI: 10.1214/aos/1176349952

Abstract

If $S(x_1, x_2,\cdots, x_n)$ is any function of $n$ variables and if $X_i, \hat{X}_i, 1 \leq i \leq n$ are $2n$ i.i.d. random variables then $\operatorname{var} S \leq \frac{1}{2} E \sum^n_{i=1} (S - S_i)^2$ where $S = S(X_1, X_2,\cdots, X_n)$ and $S_i$ is given by replacing the $i$th observation with $\hat{X}_i$, so $S_i = S(X_1, X_2,\cdots, \hat{X}_i,\cdots, X_n)$. This is applied to sharpen known variance bounds in the long common subsequence problem.

Citation

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J. Michael Steele. "An Efron-Stein Inequality for Nonsymmetric Statistics." Ann. Statist. 14 (2) 753 - 758, June, 1986. https://doi.org/10.1214/aos/1176349952

Information

Published: June, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0604.62017
MathSciNet: MR840528
Digital Object Identifier: 10.1214/aos/1176349952

Subjects:
Primary: 60E15
Secondary: 62H20

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 2 • June, 1986
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